Why is the depth of field greater, and the image sharper, when a camera lens ige67j bs:j jk9s “stopped down” to67jjb:sg e k9j a larger f-number? Ignore diffraction.

Describe how diffraction affects the 2bsi9( fvt bsdk0by 5sw4)j ji /4x,wwstatement that the depth of field is greater and the im2 if4 0wxi)td s4wbw5bvb ,9jykjss/( age sharper when a camera lens is “stopped down” to a larger f-number.

Why must a camera lens be moved farther from the film to focus on nw b4.h. +arx* t (xi6+i7mj wjhke/6nukc;fk a closer objectm.aw u6k/fx7w+*+ nrn; cb6ekxih ikt .(jhj4?

Why are bifocals neededw +7luuq4lc4kcyl 4(q mainly by older persons and not generally by younger people?4lu cl 44qw(c7 kqly+u

  Will a nearsighted person who wears corrective lens sfz3. onvs ymppg 9i/s*+l-g.es in her glasses be able to see clearly underwater when wsigo /nv9pm-py gls+f.* .s 3zearing those glasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person is nearsightedw6l6cax;2rp/u0 z(y pdrxj a2 or farsighted by looking at the width of the face through their glasses. If the person’s face appears narrower through the glasses (Fig. Below), is the person farsighteda;p2 d 2uayp6(jxw xr6z l0cr/ or nearsighted?

In attempting to disceid- (ie9a/thh+ty-h9r 3j cl ern distant details, people will sometimes squint. Why does thi icey +d 9/h3are-tlti(9j-hhs help?

Is the image formed on the 4/8 wt2tvz j4z,tt byoretina of the human eye upright or inverted? Discuss the implications of this for o4 v2ojtzt , 8b/4twytzur perception of objects.

The human eye is much like a camera — yet, when a camera shuinu:w q4sh 97zos+4o/byk,m )bdid;itter is left open and the camera is moved, the image will be blurred; but when you move your head with your eyes open,ykib4isi)dh4q : 9bo7mzu ons w,d;+/ you still see clearly. Explain.

  Reading glasses use converging lenses. A simple magnifier is also a convergkvq 2q oc.6xkq ; biuu34pz:m;ing lens. Are reading glasses therefore 3x q46.i p;b 2ukvq :uqomkz;cmagnifiers? ----待选择----yesno  Discuss the similarities and differences between converging lenses as used for these two different purposes.

Inexpensive microscopes for children’s use usually produce images 7d6 s0fxc7j(oz dow 6wthat are colored at the edges. oxd66fs d7j7 zc0(wwo Why?

Spherical aberration in a thin lens is min f kqx+ca 69drrf*94coimized if rays are bent equally by the two surfaces. If a planoconvex lens is used to form a real image of an object at inffcck rr axq9*+d4o69finity, which surface should face the object? Use ray diagrams to show why.

Which aberrations present in a simple lens are not present (or are g ikag+fc. pca v 8.nvwbi3s23,reatly reduca2.vk38vacg wi3f.b,+ispc ned) in the human eye?

Explain why chromatic aberration occurs for thin lenses but ny:cfuz;.k9+vn;n usrmlf7irk z9u, 2ot for mirrors.

  By what factor can you imbs 3 qxg4oe2i7prove resolution, other things being equal, if you use blue li7gsbexq24 o 3ight ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advant,n q y*95wjg vcn.lyf-ages for the use of large reflecting mirrors in astronomical telescopeyn5 qlgv-n , fj*wc9.ys.

Which color of visible light would give the best resolution in a micros1;a3 e bz,-sm*zusf9mbr fx -scope? Explsbszrfs9 ;z m*3,f 1xm--auebain.

  Atoms have diameters of abj7soo q-g oam:xzf02 +out $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has f-stoo eq6lt;;kl-o c)vl4 lps ranging from $f/1.4$ to $f/22$. What is the corresponding range of lens diaphragm diameters?    $\mathrm{mm}\leq D\leq$    $\mathrm{mm}$

  A television camera lens 8xb fsg,*lj+dhas a 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports that a camera se4 6sk/8ugedtq tting of $\frac{1}{250}\,s$ at $f/5.6$ will give a correct exposure. But the photographer wishes to use $f/11$ to increase the depth of field. What should the shutter speed be?$t_2$ = 1/   s

  A properly exposed photogra vb:jl.a a6xql92i2fd ph is taken at $f/16$ and $\frac{1}{60}\,s$ What lens opening would be required if the shutter speed were $\frac{1}{1000}\,s$? $f$/  

  If an $f$ = 135-mm telephoto lens is designed to cover object distances from 1.2 m to $\infty $, over what distance must the lens move relative to the plane of the film?    mm

  A 200-mm-focal-length lens can be adjusted so that it is 200.0 mm to 2k3 +1o.,wjit0 cg2 scxyyxou n03x*hh06.0 mm from the film. For what range of object d3o0.*,h1h2 iyo cxuctsxw0jk3xyg n+ istances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wish7y, go0ki lj(,fnhfu-es to photograph a 28-mtall tree from a distance of 58 m. Whatlffgik ,j huyo-,7 n0( focal-length lens should be used if the image is to fill the 24-mm height of the film?    mm

A “pinhole” camera uses a tiny pinhole instead of a lens. Show, usizmh/c,y8:v2 dngm. rsv jc+j3ng ray diagrams, how reasonably sharp images can be formec ,jjdgy/ 8h+ v23czsv: m.nmrd using such a pinhole camera. In particular, consider two point objects 2.0 $cm$ apart that are 1.0 m from a 1.0-mm-diameter pinhole. Show that on a piece of film 7.0 $cm$ behind the pinhole the two objects produce two separate circles that do not overlap.

  Suppose that a correct exposurej3)qa i-y7t 4 xyix(fn is $\frac{1}{250}\,s$ at $f/11$ Under the same conditions, what exposure time would be needed for a pinhole camera (Problem 8) if the pinhole diameter is 1.0 mm and the film is 7.0 $cm$ from the hole? $t_2$ = 1/   s

  A human eyeball is ab,2hz /si fyl6x b ik1ovug;3p.out 2.0 $cm$ long, and the pupil has a maximum diameter of about 8.0 mm. What is the “speed” of this lens? $ f-stop$ = f/  

  If the nearsighted person in Example 25–6 wore contact lenses correct zrbs ;3v9nv,e-nx 1a ;98o5 9hkg;piuioltnbed for the fng;vn9l 5ohnvurtz;9xo3abs, bkp1 ;i9-e8 iar point $(=\,\infty)$ show that the near point would be 41 $cm$. (Would glasses be better in this case?) glasses would be  ----待选择----betterworse 

  Reading glasses of what power are needed for a xhl 0rpk -;cu+person whose near point is 115 $cm$, so that he can read a computer screen at 55 $cm$? Assume a lens–eye distance of 1.8 $cm$.+    D

  A person has a far point offeh5a9rs weuh/4( :99 ld ytneej*6hi 14 $cm$. What power glasses would correct this vision if the glasses were placed 2.0 $cm$ from the eye?    What power contact lenses, placed on the eye, would the person need?   

  A person struggles to read by holdi/)sdv x m gz2fk(1p-c8axf7i zng a book at arm’s length, a distance of 45 $cm$ away (= near point). What power of reading glasses should be prescribed for him, assuming they will be placed 2.0 $cm$ from the eye and he wants to read at the normal near point of 25 $cm$? +    D

  A person’s left eye is correc.3 -t/ wdxugqgted by a $-3.50-diopter$ lens, 2.0 $cm$ from the eye.
(a) Is this person’s left eye near- or farsighted?  ----待选择----nearsightedfarsighted 
(b) What is this eye’s far point without glasses?    cm

  A person’s right eye can see objects clearly only if they are betpx2jx2 ; bf.elween 25 $cm$ and 75 $cm$ away.
(a) What power of contact lens is required so that objects far away are sharp? -    D
(b) What will be the near point with the lens in place?    cm

  About how much longer is the nearhwsp:2pec35zl4ywq **i7 jj jqtc0 ;;c gdl/dsighted eye in Example 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s ))cn k/u.roqs eyeglasses has a focal length of $-22.0 \, cm$ and the lens is 1.8 $cm$ from the eye. If the person switches to contact lenses that are placed directly on the eye, what should be the focal length of the corresponding contact lens?    cm

  What is the focal length of the eye–lens system when viewin2v zyo*u. ,tkai rn;,wg an object
(a) at infinity,    cm
(b) 33 $cm$ from the eye? Assume that the lens–retina distance is 2.0 $cm$.   cm

  A nearsighted person has f+ku-+ivjw ..5 8b i7,ghl lcaua mt8qnear and far points of 10.0 and 20.0 $cm$, respectively. If she puts on contact lenses with power $P\,=\,-4.00D$, what are her new near and far points?
near point    cm
far point    cm

  What is the magnification of a lens d7b op qyaxy9x76yd)0sx x+1yused with a relaxed eye if its focal length is b6xx 1px) y7 aydsyx9qyo0d7+12 $cm$? =    $\times$

  What is the focal length of a magnify gu1 o0xu1opg9ps wh2-ing glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated atg56rq64i661u w1ox r lp ual0lghzew9 $2.5\times$for a normal eye focusing on an image at the near point.
(a) What is its focal length?    cm
(b) What is its focal length if the $2.5\times$ refers to a relaxed eye?    cm

  Sherlock Holmes is using agws,0dh( xjy7-7 tkxx 9.00-$cm$-focal-length lens as his magnifying glass. To obtain maximum magnification, where must the object be placed (assume a normal eye), and what will be the magnification?
$d_o$ =    cm from the lens
M =    $\times$

  A 3.30-mm-wide beetle is viewed with aq bli)x +bzv:m v/e(;w 9.50-$cm$-focal-length lens. A normal eye views the image at its near point. Calculate
(a) the angular magnification, =    $\times$
(b) the width of the image,    mm
(c) the object distance from the lens.    cm from the lens

  A small insect is placed 5.5r8;x-mjouztr;x zigcx( js .j6j a5-85 $cm$ from a $+6.00-$cm$-focal-length$ lens. Calculate
(a) the position of the image,    cm
(b) the angular magnification. =    $\times$

  A magnifying glass wit4g73g , (bctvwy7whu bh a focal length of 8.5 $cm$ is used to read print placed at a distance of 7.5 $cm$. Calculate
(a) the position of the image;    cm
(b) the angular magnification. =    $\times$

  A magnifying glass is rlz1nin h)o2s n6tz 1sdk e78+kated at $3.0\times$ for a normal eye that is relaxed. What would be the magnification of this lens for a relaxed eye whose near point is
(a) 55 $cm$, =    $\times$
(b) 16 $cm$? Explain the differences. =    $\times$

  What is the magnification of an astronomical telescope whose obyrm15fq rb9(br**kj djective lens has a focabdjr *( 5k 9bmf1q*yrrl length of 76 $cm$ and whose eyepiece has a focal length of 2.8 $cm$? What is the overall length of the telescope when adjusted for a relaxed eye?
M =    $\times$
L =    $\times$

  The overall magnificak hg-dugyd9+xg lu* *.r4g3wy tion of an astronomical telescope is desired to be 25$\times$. If an objective of 78$-cm$ focal length is used,
what must be the focal length of the eyepiece? $f_e$ =    cm
What is the overall length of the telescope when adjusted for use by the relaxed eye? L =    cm

  An 8.0$\times$ binocular has 2.8$-$cm$-focal-length$ eyepieces. What is the focal length of the objective lenses?    cm

  An astronomical telescope has an objective with foca6rcyawqt3 aguqz 0iarw+ 9 -89l length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has itsurcwpc0:s7)s 58l kls two lenses spaced 75.2 $cm$ apart. If the objective lens has a focal length of 74.5 $cm$, what is the magnification of this telescope? Assume a relaxed eye. =    $\times$

  A Galilean telescope adjusted for a relaxfkx;q99kqpv;zj7wd )g u m1j 7r n8k9ced eye is 32.8 $cm$ long. If the objective lens has a focal length of 36.0 $cm$, what is the magnification? =    $\times$

  What is the magnifying power of an astronomical telescope using a reft-rwl e g5p,x9lecting mirror whose radius of cur te-p9, wlx5rgvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appeal j .v0f.p xx;n.kdj6krs to be magnified 120$\times$ by a reflecting astronomical telescope with an eyepiece having a focal length of 3.2 $cm$. What are the focal length and radius of curvature of the main (objective) mirror? M =    m r =    m

  A 170$\times$ astronomical telescope is adjusted for a relaxed eye when the two lenses are 1.25 m apart. What is the focal length of each lens?
$f_e$ =    mm
$f_o$ =    m

  A reflecting telescope (Fig. Below) hasz gmi5he7jm; : (wd/du a radius of curvature of 3.0 m for its objective mirror and a radius o d 5jue7m:/ zwg(;mdihf curvature of $-1.50m$ for its eyepiece mirror. If the distance between the two mirrors is 0.90 m, how far in front of the eyepiece should you place the photographic film to record the image of a star? $d_{2i}$ =    m

  A microscope uses an eye +brujkp0:/z n:jk c.q(jiua3 piece with a focal length of 1.40 $cm$. Using a normal eye with a final image at infinity, the tube length is 17.5 $cm$ and the focal length of the objective lens is 0.65 $cm$. What is the magnification of the microscope? =    $\times$

  A 620 $\times$ microscope uses a 0.40-$cm$-focal-length objective lens. If the tube length is 17.5 $cm$, what is the focal length of the eyepiece? Assume a normal eye and that the final image is at infinity. $f_e$ =    cm

  A 17-$cm$-long microscope has an eyepiece with a focal length of 2.5 $cm$ and an objective with a focal length of 0.28 $cm$. What is the approximate magnification?    $times$

  A microscope has a 12v*rpd b48vhn3s* :fhwn-* mas.0$times$ eyepiece and a 59.0$times$ objective lens 20.0 $cm$ apart. Calculate
(a) the total magnification,    $times$
(b) the focal length of each lens, $f_e$ =    cm $f_o$ =    cm
(c) where the object must be for a normal relaxed eye to see it in focus. $d_o$ =    cm

  A microscope has a 1):z g 3hkftmc-52rhyi .8-$cm$-focal-length eyepiece and a 0.80-$cm$ objective lens. Assuming a relaxed normal eye, calculate
(a) the position of the object if the distance between the lenses is 16.0 $cm$, $d_{oo}$ =    cm
(b) the total magnification.    $times$

  Repeat Problem 61 assuming that the fi-ev1 s - +fxtib+ifb)6 ue.faonal image is located 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound microscope has a focal length o(()n6pe nqaoz f 2.70 $cm$, and the objective lens has $f=0.740\mathrm{~cm}$. If an object is placed 0.790 $cm$ from the objective lens, calculate
(a) the distance between the lenses when the microscope is adjusted for a relaxed eye, $l$ =    cm
(b) the total magnification.    $\times$

  An achromatic lens is made of two very1n 7xmyv xi1rajr4; 7xk;as3 r thin lenses, placed in contact, that have focal lengths ofar7 xjmsr3x av r;;x14nyk17i $f_1=-28\mathrm{~cm}$ and $f_2=+23\mathrm{~$cm$}.$
(a) Is the combination converging or diverging?  ----待选择----convergingdiverging 
(b) What is the net focal length?    m

  Let’s examine spherical aberration in a particular situationhtlt0(k 9e yyu.4xra5. A planoconvex lens of index of refraction 1.50 and radiusu(49ax lr y etty50k.h of curvature $R=12.0\mathrm{~$cm$}$ is shown in (Fig. Below). Consider an incoming ray parallel to the principal axis and a height h above it as shown. Determine the distance d, from the flat face of the lens, to where this ray crosses the principal axis if
(a) $h=1.0\mathrm{~$cm$},$ $d_1$ =    cm
(b) $h=6.0\mathrm{~$cm$},$ $d_2$ =    cm
(c) How far apart are these “focal points”? $\Delta d$ =    cm
(d) What is the radius of the “circle of least confusion” produced by the $h=6.0-\mathrm{~$cm$},$ ray at the “focal point” for $h=1.0\mathrm{~$cm$},$? r =    cm

  What is the angular resolution limit (degrees) set by diffraction for the 100j f;. 2i(dwxbm ,,9acp bcvj*l-in. bvj cx(c iwp 9j*d l;a,b,fm.2(254-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a tsrdh6m3 a9 f4pelescope that can resolve features 7.0 $km$ across on the Moon, 384,000 $km$ away. You have a 2.0-$m$-focal-length objective lens whose diameter is 11.0 $cm$.
What focal-length eyepiece is needed if your eye can resolve objects 0.10 $mm$ apart at a distance of 25 $cm$? $f_e$ =    cm
What is the resolution limit (radians) set by the size of the objective lens (that is, by diffraction)?
Use $\lambda=550\mathrm{~nm.}$ $\theta$   $ \times10^{ -6}\;rad$

  The normal lens on a 35-mm camera has a fochzk- n )-s1nri ca-ec*va ;8ysal length of 50.0 $mm$. Its aperture diameter varies from a maximum of 25 $mm$ $(f/2)$ to a minimum of 3.0 mm $(f/16)$. Determine the resolution limit set by diffraction for $f/2$ and $f/16$. Specify as the number of lines per millimeter resolved on the film. Take $\lambda=550\mathrm{~nm.}$
For $\frac{f}{2}$ we have $\frac{1}{RP_2}$ =    lines/mm
For $\frac{f}{16}$ we have $\frac{1}{RP_2}$ =    lines/mm

  Two stars 15 light-years a2d6x9gzmr*, v1 dykyvx( 3eeuway are barely resolved by a 55-$cm$ (mirror diameter) telescope. How far apart are the stars? Assume $\lambda=550\mathrm{~nm.}$ and that the resolution is limited by diffraction.   $ \times10^{11 }\;m$

  (a) How far away can a human eye 2odemqk6 i /w(x aa+e.distinguish two car headlights 2.0 $m$ apart? Consider only diffraction effects and assume an eye pupil diameter of 5.0 $mm$ and a wavelength of 550 $nm$.
L =    km
(b) What is the minimum angular separation an eye could resolve when viewing two stars, considering only diffraction effects? In reality, it is about of arc. Why is it not equal to your answer in (b)? $\theta$ =    $\times 10^{-3}$ $^{\circ}$

  The Earth and Moon are separatedrdavs1g+1n 9p by about $400\times10^6\mathrm{~m.}$ When Mars is $8\times10^{10}\mathrm{~m}$ from Earth, could a person standing on Mars resolve the Earth and its Moon as two separate objects without a telescope? Assume a pupil diameter of 5 $mm$ and $\lambda=550\mathrm{~nm}.$  ----待选择----yesno 

  X-rays of wavelength 0.133 nm fall on a crystal whoseb4p wm igpw61yv ,xge/,w(n;h atoms, lying in planes, are spacyhp1g4wv,, n pw ibeg(x/mw6; ed 0.280 $nm$ apart. At what angle \phi (relative to the surface, Fig. Below) must the X-rays be directed if the first diffraction maximum is to be observed? $\phi $ =    $^{\circ}\,$

  X-rays of wavelength 0.0973 nm are d:w-1koq (m rluirected at an unknown crystal. The second diffraction maximum is recorded when the X-rays are directed at an angle ofrq ku: -o(lmw1 $\mathrm{23.4°}$ relative to the crystal surface. What is the spacing between crystal planes? d =    nm

  First-order Bragg diffraction is observed a.sajruktw013r + n 5ict $\mathrm{25.2°}$ related to the crystal surface, with spacing between atoms of 0.24 $nm$.
(a) At what angle will second order be observed? $\phi_2 $=    $^{\circ}\,$
(b) What is the wavelength of the X-rays? $\lambda $ =    nm

  (a) Suppose for a conventional X-ray image that the X-ray bealz7eawo9h y to l7m;i3tg9 ,fs.m v4b/m consists of parallel rays. What would be the magvlgole,9smh37 f7wizyt/o4a ;m.9bt nification of the image? a the magnification is   
(b) Suppose, instead, the X-rays come from a point source (as in Fig. Below) that is 15 $cm$ in front of a human body 25 $cm$ thick, and the film is pressed against the person’s back. Determine and discuss the range of magnifications that results. $m_1$ =    the magnification is  

  Sam purchases $+3.50-diopter$ eyeglasses which correct his faulty vision to put his near point at 25 $cm$. (Assume he wears the lenses 2.0 $cm$ from his eyes.)
(a) Calculate the focal length of Sam’s glasses.    cm
(b) Calculate Sam’s near point without glasses. his near point is    cm
(c) Pam, who has normal eyes with near point at 25 $cm$, puts on Sam’s glasses. Calculate Pam’s near point with Sam’s glasses on.    cm from her eyes

  As early morning passed towardz0mw(ou znw*xc +7k4 u midday, and the sunlight got more intense, a photographer notwcuzu*o70(m4 xwnk+ zed that, if she kept her shutter speed constant, she had to change the $f$-number from $f/5.6$ to $f/22$. By what factor had the sunlight intensity increased during that time? $I_2$ =    $I_1$

Show that for objects cw ntpa q2bs8e/ ),l0tgcu3v;very far away (assume infinity), the magnification of a camera lengl;c2 v3 tp8c0uq)/ew ,s bants is proportional to its focal length.

  For a camera equipped with a1),t cmxoko82mlu.r5j+a+ ad r be)dd 50-$mm$-focal-length lens, what is the object distance if the image height equals the object height? How far is the object from the film?
$d_o$ =    mm
d =    mm

  A woman can see clearly with her right eye only when objects ar .gtvqf 3lmo/0e between 45 $cm$ and 155 $cm$ away. Prescription bifocals should have what powers so that she can see distant objects clearly (upper part) and be able to read a book 25 $cm$ away (lower part) with her right eye? Assume that the glasses will be 2.0 $cm$ from the eye.
$P_1$ =    D(upper part)
$P_2$ =    D(lower part)

  A child has a near poi2) wq9g akzwamwe ,4k+nt of 15 $cm$. What is the maximum magnification the child can obtain using an 8.0-$cm$-focal-length magnifier? What magnification can a normal eye obtain with the same lens? Which person sees more detail?
$M_1$ =    $\times$
$M_2$ =    $\times$

  What is the magnifying m,jr 8evwl-- lpower of a $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mountains trit 8cxz en kv1pt/).az9es to make a telescope using the lenses from his readpcz)k/.9ntza evtx18ing glasses. They have powers of $+2.0-D$ and $+4.0-D$, respectively.
(a) What maximum magnification telescope is possible? $M$ =    $\times$
(b) Which lens should be used as the eyepiece?    D

  A 50-year-old man useso,tlx q3m. n+a /difj2 $+2.5-diopter$ lenses to read a newspaper 25 $cm$ away. Ten years later, he must hold the paper 35 $cm$ away to see clearly with the same lenses. What power lenses does he need now in order to hold the paper 25 $cm$ away? (Distances are measured from the lens.) $P_2$ = +    D

  Spy planes fly at extremely high altitudes l2t+ei xau 4:d.8gkmh (25 $km$) to avoid interception. Their cameras are reportedly able to discern features as small as 5 $cm$. What must be the minimum aperture of the camera lens to afford this resolution? (Use $\lambda=550\mathrm{~nm}.$)D =    cm

When shooting pictures at very short distances, exposurene vy-nb,(y +z times must be increased because of the increased distance of the lens from the fi+byyvnz, -ne (lm for a focused image.
(a) Show that when the object is so close to the camera that the image height equals the object height, the exposure time must be four times longer (or 2 f-stops) than when the object is a long distance away (say, $$\infty), given the same illumination and f-stop.
(b) Show that if $d_o$ is at least four or five times the focal length f of the lens, the exposure time is increased by less than half an f-stop relative to the same object being a great distance away.

  The objective lens akps3 7xtygc hxi*27cn / io8cqtc4wrr w)k,.(nd the eyepiece of a telescope are spaced 85 $cm$ apart. If the eyepiece is $+23$ diopters, what is the total magnification of the telescope? $M$ =    $\times$

  The Hubble Space Telescope, with an objective diameter of 2.uf) eob k9n2m0nkit3z/c. ,h t4 m, is viewing the Moztuh 0mcf.ten b3,)9/o2i knkon. Estimate the minimum distance between two objects on the Moon that the Hubble can distinguish. Consider diffraction of light of wavelength 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses, onewl 2.vf 0irg.l84jsm y with $f=4.0\mathrm{~cm}$ and the other with $f=44\mathrm{~cm}$ are made into a telescope.
(a) What are the length and magnification? Which lens should be the eyepiece?
The distance between the two lenses is   cm
M =    $\times $
f =    cm
(b) Assume these lenses are now combined to make a microscope; if the magnification needs to be $25\times,$ how long would the microscope be?    cm

  An astronomical telescope has a magnifi*klo n0wdxjh9 .kzpv;n oi9 hxi).u-/cation of 8.0. If the two lenses are 28 $cm$ apart, determine the focal length of each lens.
The focal length of the eyepiece lens is    cm
The focal length of the objective lens is    cm

  You want to design a spy satellite to photograph license pjd*;* 8b zo kreyn1ly+late numbers. Assuming it iy*j*dnzby rk+lo8 ; e1s necessary to resolve points separated by 5 $cm$ with 550-$nm$ light, and that the satellite orbits at a height of 130 $km$, what minimum lens aperture (diameter) is required? D =    m

  A Lucite planoconvex :lk(tj ( t1 mye nx7a:5a9g jzh2t4w2qqjyp8zlens (Fig. Below) has one flat surface and the other has $R=18.4\mathrm{~cm}.$ This lens is used to view an object, located 66.0 $cm$ away from the lens, which is a mixture of red and yellow. The index of refraction of the glass is 1.5106 for red light and 1.5226 for yellow light. What are the locations of the red and yellow images formed by the lens? $d_{i\,red}$ =    cm
$d_{i\,orange}$ =    cm